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Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 125v

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.79.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 126r); this page is its left half.

The machine reads it as

  1. a+ b aqu a + Z a b + 2. 5-1 a b + 22 2 a b + 2F12. 723,
  2. sit Laequ L. fiet.
  3. Si Zaequ fiet:
  4. in decimalibus si addas
  5. duplum orom esti
  6. 1 + i
  7. 3141 + 3, - 1
  8. 4-
  9. 12
  10. 1, 2,3
  11. X 1672
  12. 1,23, 4
  13. asy 5
  14. 4 4
  15. ab+ 2722 a b+ 2Ea
  16. + 2567 2
  17. n nominatores progressionis Geometricae triplae, et ita porro. Quare utia est in numeris adhiberi algorithmum dyadicum pro extractione
  18. radicis quadratae, ternarium pro extractione radicis cubicae. Et nihil ominus semper apparebit ratio transferendi ex una in alteram,
  19. Caelerum ex his etiam apparebit quomodo nomina numeratores procedere debeant
  20. - 1
  21. 1 + 008 aequ 14 0001 A = 0000001.
  22. 81
  23. 4 0000009001
  24. 10
  25. 24373
  26. ese
  27. d082304537a
  28. aequ 1 +000051D8DB. - 0000 0BD12500 +00000000000b250V erc summa
  29. + 280
  30. 1d C)) 8)50bC
  31. sit l+ e. cujus cubus l + 31 e + 3le + e. dividatur in duas partes l + 3le, et C + 3e l. ex quibus prior fiat aequal. a. posterior aequal. b. et quaeritur (7) a + b
  32. seu radix cubica ex 13+ 3le + e + 3C12. id est quaeritur l. e. Series proveniet hujus modi:
  33. 3+1 + e
  34. er. 25.
  35. 80 se
  36. B) Pt 3e ( 3el
  37. mtn aequ. 1. 01
  38. m +n. aequ m + 2mn+ n. sit maequ. 1. et n aequ fiet: mn aequ, 1 + or + 001 aequ 1. jam, 2 aequ 10 fiet 1 + 010 + 001. aequ 1. 011 quod est quadr. de 1. 01
  39. V + 21 laequ. 1 + ot aequ. 1 + e2 - 00 441
  40. 10601
  41. 10001000
  42. avs100100001
  43. 100100001
  44. 10001
  45. 100500001
  46. l
  47. 1+01 sit seu + + et 1 + 0110 + oi ( 1. + 1 + 0b1 aequ AB. t 1001
  48. Y 1 + ou aequ. 1 + 001 00 001001 + 00000011011 cu equ
  49. (10 equ 10 00 t +
  50. 2)raequ Y10. aequ
  51. 10001
  52. . 100 1000110001
  53. 6
  54. dobodd
  55. 0011b00101 f+H
  56. Y 10. 01 aequ (, 4101 aqu , + 0101
  57. Nhabeatus una Radix ejus _ R - p R - q. hunc
  58. subtuhendo a priore fieri X R3 - p X + pR aequ. 0.
  59. + 10010001
  60. - 0000000100100001
  61. = 10010000
  62. 00000vVOVVOIIe
  63. dividendo per X -R. fiet: X + R X + R aequ. 0.
  64. et X aego +RX + p p - Z N et x + = R B Y p - 2 t seu Xp Sp. 2 f - L R
  65. At aequ. = 1 + s.3 Exgo E si jame . multipiretur per 3 quia h. 1 idem quod R.
  66. recte multiplicari potest
  67. ero et Yh, idem quod ith in c. ergo quia S1 nes habet valores unum 1. alteropndios - 1 4+S.3
  68. etiam 3str duos habebit natores, unum h. alterum Th in alterum YE in =1 + sa
  69. Hinc quique 35 + s- 2 aequ. - 1 +. s - 2. multiplicando per - 1 4 f.3 fict: + L 4, sa3 -+ s. 14 1 s6
  70. 5+ f- 2 aequ. L + V- - s. 4 (3 Eodemmodo S5+ s. 2 aequ- 1 + Su2 nulti per - 1 + f.3
  71. 5 = S.2 aequ. L = s. 3 + Y-=
  72. +13
  73. Ergo 25 5. Y- 2 + Y5 - S. 2 aequ. 1 f 16. quod
  74. em, nam extidendo radice eu his duobu binonous X
  75. i
  76. 1100 ( +qu. V + 0010001 aequ. l _ + 00010001 = 000 300O1001000D1+ 0000000VVV1001000110001
  77. x - g X - pX - quequ. 0.
  78. ve
  79. 2440, xqu. 16,
  80. +
  81. unde puto nominalores semper non alios forequam progressionis Geometricae duplae
  82. + 3
  83. aesi atb 3r an BZa
  84. fiet:
  85. 10001
  86. 000
  87. seriem infinitam prodiit: 3. +49 ex) id est 1+ 16. est
  88. curtium binomium multiplicandum per V =1 Sad
  89. rarilibus. Regula vulgaris.. ne
  90. 72913
  91. +10000d00000000000000
  92. + 0000500000
  93. 0000000 125000
  94. 00
  95. At ∞
  96. 00
  97. + 1
  98. 101 c
  99. 10
  100. 0001
  101. 101

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 125v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068124:0252?run=73